### Cow and Exercise

Farmer John is obsessed with making Bessie exercise more! Bessie is out grazing on the farm, which consists of $n$ fields connected by $m$ directed […]

Farmer John is obsessed with making Bessie exercise more! Bessie is out grazing on the farm, which consists of $n$ fields connected by $m$ directed […]

Bessie is planning a vacation! In Cow-lifornia, there are $n$ cities, with $n-1$ bidirectional roads connecting them. It is guaranteed that one can reach any […]

You are given two integers $n$ and $m$ ($m < n$). Consider a convex regular polygon of $n$ vertices. Recall that a regular polygon is a polygon […]

Suppose you are performing the following algorithm. There is an array $v_1, v_2, \dots, v_n$ filled with zeroes at start. The following operation is applied […]

Your task is to calculate the number of arrays such that: each array contains $n$ elements; each element is an integer from $1$ to $m$; […]

You are given an array $a_1, a_2, \dots, a_n$. You can perform the following operation any number of times: Choose a pair of two neighboring […]

The Red Kingdom is attacked by the White King and the Black King! The Kingdom is guarded by $n$ castles, the $i$-th castle is defended […]

You are given a set of strings $S$. Each string consists of lowercase Latin letters. For each string in this set, you want to calculate […]

Given 2 integers $u$ and $v$, find the shortest array such thatÂ bitwise-xorÂ of its elements is $u$, and the sum of its elements is $v$. Input […]

You are given a tree consisting of $n$ nodes. You want to write some labels on the tree’s edges such that the following conditions hold: […]

It’s the year 5555. You have a graph, and you want to find a long cycle and a huge independent set, just because you can. […]

You are given an array $a$ of length $n$ that has a special condition: every element in this array has at most 7 divisors. Find […]

You are given two integers $n$ and $k$. Your task is to find if $n$ can be represented as a sum of $k$ distinct positive odd (not […]

You are given a colored permutation $p_1, p_2, \dots, p_n$. The $i$-th element of the permutation has color $c_i$. Let’s define an infinite path as infinite sequence […]

Petya has a rectangular Board of size $n \times m$. Initially, $k$ chips are placed on the board, $i$-th chip is located in the cell […]

You wrote down all integers from $0$ to $10^n – 1$, padding them with leading zeroes so their lengths are exactly $n$. For example, if […]

The King of Berland Polycarp LXXXIV has $n$ daughters. To establish his power to the neighbouring kingdoms he wants to marry his daughters to the […]

You are given a string $S$ and an array of strings $[t_1, t_2, \dots, t_k]$. Each string $t_i$ consists of lowercase Latin letters from a to n; $S$ […]

You are given three integers $n$, $k$, $m$ and $m$ conditions $(l_1, r_1, x_1), (l_2, r_2, x_2), \dots, (l_m, r_m, x_m)$. Calculate the number of […]